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arXiv · 1606.00289

Enumerating simple paths from connected induced subgraphs

Pierre-Louis Giscard·Paul Rochet
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Abstract

We present an exact formula for the ordinary generating series of the simple paths between any two vertices of a graph. Our formula involves the adjacency matrix of the connected induced subgraphs and remains valid on weighted and directed graphs. As a particular case, we obtain a relation linking the Hamiltonian paths and cycles of a graph to its dominating connected sets.

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Pierre-Louis Giscard, Paul Rochet. 2017-12-05. Enumerating simple paths from connected induced subgraphs. https://doi.org/10.1007/s00373-018-1966-9

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